Let \(\mathrm{f}(\mathrm{~A}, \mathrm{~B})=\overline{\mathrm{A}}+\mathrm{B}\), Simplified expression for function f (f (x y, y), z) is :

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NIELIT Scientific Assistant CS 5 Dec 2021 Official Paper

Answer 1

The Correct answer is : Option 4

Given:

Function definition: f(A, B) = A + B

We need to evaluate: f(f(xy, y), z)

Step 1: Compute the inner expression f(xy, y)

Using the function definition:

f(xy, y) = xy + y

Apply De Morgan's Law:

xy = x + y

So:

f(xy, y) = (x + y) + y

Simplify:

y + y = 1 ⇒ x + 1 = 1

Therefore, f(xy, y) = 1

Step 2: Compute the outer expression f(1, z)

f(1, z) = 1 + z = 0 + z = z

Final Answer: z

Correct Option: Option 4: None of the options, since none of them simplify to just z.